Elementary arithmetic is the simplified portion of arithmetic which includes the operations of addition, subtraction, multiplication, and division.
Elementary arithmetic starts with the natural numbers and the written symbols (digits) which represent them. The process for combining a pair of these numbers with the four basic operations traditionally relies on memorized results for small values of numbers, including the contents of a multiplication table to assist with multiplication and division.
A numeral system (or system of numeration) is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
Ideally, a numeral system will:
In computing, an arithmetic and logic unit (ALU) is a digital circuit that performs integer arithmetic and logical operations. The ALU is a fundamental building block of the central processing unit of a computer, and even the simplest microprocessors contain one for purposes such as maintaining timers. The processors found inside modern CPUs and graphics processing units (GPUs) accommodate very powerful and very complex ALUs; a single component may contain a number of ALUs.
Mathematician John von Neumann proposed the ALU concept in 1945, when he wrote a report on the foundations for a new computer called the EDVAC. Research into ALUs remains as an important part of computer science, falling under Arithmetic and logic structures in the ACM Computing Classification System.